This paper provides the limit theory of real time dating algorithms for bubble detection that were suggested in Phillips, Wu and Yu (2011, PWY) and Phillips, Shi and Yu (2013b, PSY). Bubbles are modeled using mildly explosive bubble episodes that are embedded within longer periods where the data...

This paper presents a nonparametric and distribution-free estimator for the function h*, of observable exogenous variables, x, in the generalized regression model, y-G(h*(x), mu). The method does not require a parametric specification for either the function h* or for the distribution of the...

This paper presents several generic uniform convergence results that include generic uniform laws of large numbers. These results provide conditions under which pointwise convergence almost surely or in probability can be strengthened to uniform convergence. The results are useful for...

We consider the problem of estimating the conditional distribution of a post-model-selection estimator where the conditioning is on the selected model. The notion of a post-model-selection estimator here refers to the combined procedure resulting from first selecting a model (e.g., by a model...

This paper considers the linear regression model with multiple stochastic regressors, intercept, and errors that have undefined means. This model is of interest from a robustness perspective as a polar case. Generally, least squares estimators are inconsistent in this context. It is shown,...

Reduced rank regression (RRR) models with time varying heterogeneity are considered. Standard information criteria for selecting cointegrating rank are shown to be weakly consistent in semiparametric RRR models in which the errors have general nonparametric short memory components and shifting...

This paper develops a semiparametric method for estimating the nonrandom part V(.) of a random utility function U(v, omega) - V(v) + e(omega) from data on discrete choice behavior. Here v and omega are, respectively, vectors of observable and unobservable attributes of an alternative, and...